In this paper, the non-global solvability of the Cauchy problem for non-gauge invariant semilinear semirelativistic equations is considered. The lifespan estimate has been considered based on the analogy of semilinear Schrödinger equations and will be determined by the scaling property of semilinear semirelativistic equations. On the other hand, in this paper, in the one-dimensional case, a sharper lifespan estimate is given by a simple argument of weak form with special test functions. Specifically, this lifespan estimate follows from the conjecture of advection equations instead of the scaling property of semilinear semirelativistic equations.

中文翻译：

---

一维非规范不变半线性半相对论方程的寿命估计

本文考虑了非规范不变半线性半相对论方程柯西问题的非全局可解性。寿命估计是基于半线性薛定谔方程的类比考虑的，并将由半线性半相对论方程的标度属性确定。另一方面，在本文中，在一维情况下，通过具有特殊测试函数的弱形式的简单参数给出了更清晰的寿命估计。具体来说，这个寿命估计来自对流方程的猜想，而不是半线性半相对论方程的标度属性。